During operation, machines and their constituent components are subjected to both mechanical and thermal stresses. Individual components, for example, can be subjected to direct mechanical stresses through the application of compressive or tensile forces. Thermal stresses occur when a temperature of the machine or component exceeds an acceptable operating range or when temperature excursions within the machine or component, or in the environment in which the component operates, exceed prescribed values. Such stresses may be constant or vary as a function of time.
The components in a gas turbine, for example, are subjected to cyclic mechanical and thermal stresses, especially when the gas turbine is started up, shut down or its operating parameters significantly changed. Components of steam turbines, electrical generators and other rotating and non-rotating machines are also subjected to such thermal and mechanical stresses.
Cyclic loading, both mechanical and thermal, results in material fatigue, which, in many cases limits the service life of a machine or component. Material fatigue resulting from cyclic loading conditions may also cause the initiation and growth of material cracks. The growth of these cracks is often a life-limiting mechanism for the component. Also, small cracks can nucleate from inherent material flaws, such as a preexisting flaw in a forging or from another crack-initiation mechanism, such as low-cycle fatigue.
Cyclic loading, for example the starting and shutting down of a gas turbine or a significant change in its operating condition, may cause small cracks in a component to grow incrementally. As the crack grows it may impact the structural integrity of the component. This phenomenon is referred to as stable crack growth.
But when the crack reaches a certain critical size, its growth becomes unstable (i.e., uncontrolled growth). The unstable crack grows quickly and significantly, possibly resulting in component failure.
The number of cycles N at which unstable crack growth begins is called the fatigue crack life of the component. The crack growth rate, which directly impacts the value of N, can be estimated using linear elastic fracture mechanics (LEFM) and finite element analyses (FEA) for estimating a transient stress field to which the component is subjected.
Due to the uncertainties associated with material properties and initial flaw size and the complexities of the LEFM and FEA analyses, estimating the crack growth rate and thereby a service life of a component is a difficult and tedious process. Therefore, the design of some components may not consider fatigue crack growth or the design may be extremely conservative relative to fatigue crack growth. As a result of such conservative approaches, the component may be designed with conservative features (e.g., material, dimensions, tolerances, etc.), its operating conditions may be limited (e.g., minimum starting metal temperatures), or it may be prematurely inspected, serviced, or taken out of service, i.e., good components are discarded due to overly conservative assumptions. These premature service intervals or premature component replacements tend to add significantly to system cost. A more accurate analysis of fatigue crack growth would permit a longer interval between component servicing and/or a longer useful service life for the component.
Fatigue crack life calculations can be performed using a deterministic or a probabilistic approach.
Traditional deterministic calculations of fracture mechanics (FM) service life of a component, such as a gas turbine rotor disc, result in conservative values as a means to compensate for various unknowns in the deterministic approach. This approach uses minimum (or maximum as appropriate) material properties to estimate a component service life. Conservative estimates of material properties and initial flaw sizes are used, as well as worst-case scenarios and significant safety factors. Using these assumptions, the fatigue crack life of the component is then conservatively estimated by LEFM or known extensions of that technique. Generally the fatigue crack life is measured in years of operation or number of component cycles (e.g., start-ups and shut-downs).
As applied to a gas turbine rotor disc, these conservative estimates may cause unnecessary replacement of a disc or may suggest considerable over-design of discs. These scenarios result in decreased service life and increased life cycle costs of gas turbine rotors. Also, the conservative approach schedules service inspections based on availability and the capabilities of inspection techniques, rather than on inspections that are required to reduce the risks of continued component operation.
For instance, a gas turbine includes, according to one design, about twenty rotor discs (also referred to as compressor discs or turbine discs) stacked horizontally end-to-end to form a gas turbine rotor. See FIG. 2 and the discussion of FIG. 2 below.
The deterministic approach may yield a fatigue crack life for a rotor disc of N=3000 engine starts, for example. According to the deterministic approach, this result is based on minimal material properties and maximum assumed flaw size at the worst possible location on the rotor disc, i.e., where the stress magnitude is greatest.
This approach falls under the so-called safe-life design philosophy and has been used for land-based heavy-duty gas and steam turbines. The deterministic fracture mechanics calculations are based on extremely conservative design margins. They assume the worst case scenario in terms of manufacturing and operations; that is, the disc material will be the worst possible, a large flaw will exist in the worst location (in terms of mechanical and thermal stresses) on the disc forging, and the gas turbine is always started under extreme ambient conditions.
For example, as illustrated in FIG. 1, fracture mechanics calculations determine a service life of a rotor disc 4 by assuming that large forging flaws exist at high-stress locations identified by a reference character 5.
A drawback of employing such deterministic fracture mechanics calculations for component analysis is the use of a single component location or a few locations, and the assumption of minimum/maximum material properties at those locations. Erroneous conclusions may result from these calculations. A more realistic distribution of the material properties and flaw sizes throughout the component is not used in the deterministic approach. The safety-factor of the deterministic approach may thereby lead to an overly conservative design.
In reality, the material properties, flaw size, and flaw locations vary among rotor discs and within a disc. It is highly improbable that the largest forging flaws will be present at the most critical locations in a disc with the worst material properties.
In lieu of a deterministic approach, a probabilistic approach may yield more realistic service life values and inspection intervals. To quantify the probability of a disc failing due to a fracture, probabilistic fracture mechanics (PFM) analysis is used.
In a probabilistic analysis of gas turbine rotor discs, variations in material properties, flaw size and location distribution are used to determine a probability of failure, PoF(N), after N operational cycles. A typical probability-of-failure value for a gas turbine rotor disc after N=3000 starts is on the order of:PoF(3000)˜1/1,000,000This result indicates that after about 3000 starts, 1 of 1,000,000 rotor discs will have failed.
Advantages and disadvantages of the probabilistic and deterministic approaches have been discussed at length in the pertinent literature. Both approaches can be used to conduct failure analyses of a gas or combustion turbine and its constituent components, in particular its rotating turbine discs.
The teachings of the present invention can be applied to, for example, a gas or combustion turbine, which is one type of a internal combustion engine. The principles of the invention can also be applied to any machine that experiences stresses due to any causative agent during start-up, operation, or shut-down, such as machines comprising a heavy mass rotating at high speeds, e.g., steam turbines, turbo-pumps, and electrical generators.
A gas turbine operates by compressing and accelerating an air stream within a compressor. Fuel is injected into the air stream in a combustor or combustion chamber, where ignition of the fuel occurs. Ignition of the fuel creates a hot combustion gas flow that is directed to a turbine and causes it to rotate. The combustion gas stream (also referred to as a working gas) expands as it enters the turbine, which includes rows of stationary guide vanes and rotating blades connected to a turbine shaft. The expanding gas flow is accelerated by the guide vanes and directed over the rotating blades, causing the blades and thus the turbine shaft to spin. The spinning shaft provides a mechanical torque output and also turns the compressor. After passing through the blades and vanes the working gas flow enters a turbine exhaust casing.
FIG. 2 depicts a prior art gas or combustion turbine 10, generally including a compressor 12, a combustion chamber 14 and a turbine 16. The compressor 12 inducts and compresses ambient air. The compressed air then enters one or more combustors 28 in the combustion chamber 14, where the compressed air is mixed with fuel. The air-fuel mixture ignites to form a hot working gas. The working gas is directed to the turbine 16 where it expands through alternating rows of stationary guide vanes 22 and rotating blades 18 to generate mechanical forces that turn a shaft, which is not specifically shown in FIG. 2. The expanded gas exits the turbine 16 via an exhaust casing (not shown). The rotating blades 18 are attached to rotor discs 40 that are horizontally stacked to form a segment of the turbine shaft.